Astigmatic hybrid SU(2) vector vortex beams: towards versatile structures in longitudinally variant polarized optics

Area of Science:

• Optics and Photonics
• Structured Light
• Beam Propagation

Background:

• Conventional vector vortex beams (VVBs) possess two degrees-of-freedom (DoFs): orbital angular momentum (OAM) and polarization.
• A recent hybrid ray-wave structure introduced multiple DoFs including ray trajectory and coherent state phase.
• Generalizing structured light offers enhanced control and application potential.

Purpose of the Study:

• To generalize the hybrid ray-wave structure by introducing astigmatic degree as a new controllable DoF.
• To investigate the propagation-dependent topological evolution of these novel beams.
• To demonstrate experimental generation and control of astigmatic hybrid vector vortex beams.

Main Methods:

• Theoretical modeling of astigmatic hybrid vector vortex beams.
• Introducing astigmatic degree as a new degree-of-freedom.
• Experimental generation using a laser with combined spherical and cylindrical lenses for astigmatic conversion.

Main Results:

• Astigmatic hybrid vector vortex beams exhibit propagation-dependent transverse topology evolution.
• The topological transformation ranges from linear trajectories to complex star shapes with varying singularities.
• Control over astigmatic degree allows manipulation of polarization states and trajectory patterns.

Conclusions:

• The proposed astigmatic hybrid VVB generalizes structured light with a new controllable astigmatic degree.
• These beams demonstrate unique propagation-dependent topological evolution and tunable polarization.
• The ability to control multi-DoF patterns in a single beam significantly expands applications in optical communication, machining, and trapping.